The curve with parametric equationsx = t, y = 1 - cos t, 0 ≤ t ≤ 2πis called a sinusoid. Findthe point (x, y) where the slope of the tangent line is smallest

Q: Find the ordinate of the center of curvature of the curve y² = 4x at point (2, 4) from the x-axis.

A: Given option are wrong, option c should be '-16'.

Q: Consider the curve C parametrized by (x, y) = (3 cos (-10t), 3 sin(-10t)), for –x/2sts a/2 Then C is…

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: What is the equation of the tangent plane to the surface y = eª cos (z) at the point (1, e, 0)?

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Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

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Q: 7. Find the radius of curvature of the curve y = In sin x at x= r/2 .

A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

Q: (i) Find equations of the tangent plane and the normal line to the given surface at the specified…

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: x=e"Cost = e"S int

A: Given: x=e-tcosty=e-tsint At t=0: x=1, y=0 Differentiating both with respect to t:…

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find equation of line normal to plane 3x + 2y- z = 5 and pass through Drigin point.

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Q: At what point does the curve have maximum curvature? What happens to the curvature as x → ∞? y = ln…

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Q: Find the equation of the tangent plane to z = In(x?y) – x/ỹ at (-,4). %3D

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Q: Find the length of arc from (0,0) to (4,4) of the curve x = 2/y.

A: given curve     x=2y            we have to   find the arch length fro (0,0)  to  (4,4)now  x=2y ⇒…

Q: Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t , y = 2t, z =…

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

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Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: Find the equation of the tangent plane to the surface 3 – 12y – sin(r*:) = 0 at the point (2, 1,0).…

A: To find gradient of the function.

Q: Consider the curve C parametrized by x = -1 + 6 sin t and y 6 cos t for -n <t< 9n. %3D Then C is a…

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Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: The plane tangent to the surface z+1= ze" cos z at (1,0,0) can be represented by the equation Z= 1.…

A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…

Q: Consider the parametric curve C given by X= √x= √2+ - cos t 2y = soin't where te [0.2π] (1)…

A: (1)Given,x = 32t-cos(t)y=5sin2(t)    where    t∈0, 2πcurve C has horizontal tangent line where dydx…

Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

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Q: Find equation of line normal to plane 3x + 2y – z = 5 and pass througl Origin point.

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Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

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Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: parametrically

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Q: Find reparametri zations two Curve aLt)=(t, Cosht, o, teR.

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: ston Compute the length of the circle of radius r defined parametrically by x = 3 cost, y = 3 sint ;…

A: given that x=3 cost , y=3 sint; 0≤t≤2π find out the length of the circle of radius r i.e. arc length…

Q: Find an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

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Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

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Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Find the length of the parametric curve. X =t+ sint -T<t<π | ly=t2 + cost Set up the integral, then…

A: HEre we have to find the arc length of the given parametric curve

Q: Find the equation of the tangent plane to the surface z = ly² – lz² at the point (-2, 0, -4). 4x+0

A: Given   z=y2-x2 We have to find equation of tangent line at the point(-2,0,4)

Q: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

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